A Calibration of the 85 Peg Binary System

A&A 392, 529–533 (2002) Astronomy DOI: 10.1051/0004-6361:20020962 & c ESO 2002 Astrophysics

A calibration of the 85 Peg binary system

J. Fernandes1,P.Morel2, and Y. Lebreton3

1 Observatório Astronómico da Universidade de Coimbra, Santa Clara, 3040 Coimbra, Portugal and Departamento de Matemática da Faculdade de Ciências e Tecnologia da Universidade de Coimbra, Portugal 2 Département Cassini, UMR CNRS 6529, Observatoire de la Côte d’Azur, BP 4229, 06304 Nice Cedex 4, France 3 GEPI, Observatoire de Paris Meudon, 92195 Meudon, France

Received 28 September 2001 / Accepted 11 June 2002

Abstract. We have calibrated the initial abundances, age and mixing-length parameters of the visual binary system 85 Pegasi. We obtain an age t85 Peg = 9 345 500 Myr, masses mA = 0.88 0.01 M and mB = 0.55 0.02 M , an initial helium mass = . . Fe = − . . Λ = . . fraction Yi 0 25 0 01, an initial metallicity [ H ]i 0 185 0 054 and mixing-length parameters A 1 80 0 05 and ΛB = 2.14 0.10. We ﬁnd that, as already proposed, 85 Peg B is itself a binary. The mass of the unseen companion is mb ≈ 0.11 M .

Key words. stars: binaries: visual – stars: evolution – stars: fundamental parameters – stars: individual: 85 Peg

1. Introduction massive than 85 Peg A the brighter one (e.g. Slocum 1915; Hall 1948; Underhill 1963). This was found again by Martin & The calibration of a binary system is based on the adjustment Fe Mignard (1998) on the basis of Hipparcos observations. This of stellar modeling parameters (t?, Y , [ ] , Λ , Λ ) to the ob- i H i A B abnormal situation could be explained by the fact that 85 Peg B servational data at the age t? of the system, with the reasonable is an undetected binary. 85 Peg A is known as a metal-poor star hypothesis of a common origin for both components (same ini- and found to be much older than the Sun (Perrin et al. 1977). tial chemical composition and age). Y and [ Fe ] are, respec- i H i Because of its small mass, 85 Peg A sits close to the  Λ tively, the initial helium mass fraction and metallicity, A and which gives a constraint on its initial helium abundance, a Λ B are respectively the mixing-length parameters of the pri- value traditionally associated with primordial helium (Perrin mary A and secondary B. For each component one also infers et al. 1977; Catchpole et al. 1967; Smak 1960). a mass value consistent with theoretical stellar modeling. The photometry and the atmospheric parameters of Taking into account the most recent theoretical and 85 Peg A have been determined many times. The first spectro- observational astrometric, spectroscopic and photometric scopic determination of the metallicity is from Wallerstein & results we undertake the calibration of 85 Pegasi (HD 224930, Helfer (1959), while the most recent metallicity and effective HIP 171, BD+26 4734 4, HR 9088, β 733 ADS 17175, temperature determinations are due to van’t Veer (2000) and IDS 23569 +2633; α = 00h 02m 10s, δ =+27◦0405600 (2000)). Fulbright (2000). While 85 Peg A is a well known star, the sec- It is a well-known visual and single-lined spectroscopic binary ondary component is less well known. The greatest limitations system. The components, 85 Peg A and B, are main sequence to studying 85 Peg B in detail were the lack of individual photo- low mass stars of spectral types G5 and K7 respectively metric and spectroscopic measurements due to its proximity to (ten Brummelaar et al. 2000). The shortness of the period 85 Peg A (ρ ≈ 000. 75). Recently, ten Brummelaar et al. (2000), (≈27 years) and the proximity to the Sun (∼12 pc) give it an in- performed differential photometry in the Johnson  system teresting place among the binary stars. The visual orbit is very for both stars using adaptative optics, which allows us to deter- well known (Hall 1948). Nevertheless, some studies of the or- mine the effective temperatures and bolometric magnitudes of bit have been recently published. The latest (Söderhjelm 1999) both components. has yielded improvements to the Hipparcos trigonometric parallax and orbit, combining data from the satellite with In their pioneering work Fernandes et al. (1998) tried to ground-based observations. 85 Peg is one of the rare cases calibrate the helium abundance and age of both 85 Peg A and for which the mass ratio can be obtained by both astrometric B by means of stellar models. No solution was possible when and spectroscopic observations. For many years investigators fitting both components for the same helium and age values. have claimed that 85 Peg B, the fainter component, is more The models appeared to be hotter than the observations. The discrepancy appears to be removed if the microscopic diffusion Send offprint requests to: J. Fernandes, of helium and heavy elements, the enrichment of α-elements e-mail: [email protected] and the non- effects in the iron abundances determinations

Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20020962 530 J. Fernandes et al.: Improved calibration of 85 Peg

Table 1. Relevant orbital elements of the 85 Peg. As usual P is the orbital period in years, a the semi-major axis, i the inclination and e the eccentricity. The error bars are probable errors. S¨oderhjelm does not give the errors on the orbital elements but he indicates that the number of given decimals reﬂect the mean errors.

Author Paie Hall (1948) 26.27 0.19 000. 83 000. 02 −50◦.0 2◦.00.38 0.01 Söderhjelm (1999) 26.28 000. 83 −49◦. 0.38 are taken into account in models of low mass stars (Lebreton the adopted orbital elements and parallax, we derive the “spec- et al. 1999). Nevertheless, Lebreton et al. did not perform a troscopic” mass fraction: full calibration of 85 Peg A and did not examine the secondary B = 0.43 0.06. component. s Our purpose here is (1) to provide a complete modeling of Note the remarkable agreement between spectroscopic and the system based on more appropriate stellar models (i.e. in- photographic determinations of the mass fraction. A weighted cluding microscopic diffusion) and (2) to propose a calibration average of the photographic and spectroscopic values leads to: of the unknown parameters (age, helium, individual masses) B85 Peg = 0.44 0.02. that fulfills the recent observational constraints. The paper is divided as follows. In Sect. 2, we collect and With the sum of masses and mass fraction derived above, the discuss the observational constraints. Section 3 is devoted to masses of the components are respectively: the description of physics and modeling. We summarize and mA = 0.84 0.08 M , mB = 0.66 0.07 M , conclude in Sect. 4. showing 85 Peg A definitively to be the more massive star.

2. Observations of the visual binary 85 Peg 2.2. Spectroscopic and photometric data

2.1. Astrometric data Stellar parameters were determined from spectroscopic and photometric analysis. Table 2 lists recently published data for For 85 Peg we are in the fortunate position of having two the photometry, effective temperature and metallicity of 85 Peg. precise, self consistent and independent determinations of the For 85 Peg A we chose to retain the recent determinations trigonometrical parallax and improved orbital elements; from Fe = − . ff = [ H ] 0 69 dex and Te A 5550 K of van’t Veer (2000). these data individual masses mA and mB can be derived inde- A This T ff determination relies on the careful fit of Balmer pendently. Table 1 shows the excellent agreement of the rel- e line profiles with Kurucz’s (1991)  model atmospheres evant elements of the astrometric orbits of Hall (1948) and with the constraint that the model reproduces both the Hα Söderhjelm (1999). The first determination of the parallax is and Hβ profiles. Furthermore we point out that, according to the standard photographic parallax (Wyller 1956; Heintz 1993) Thévenin & Idiart (1999), the metallicity of metal-poor stars, based on improved orbit and several decades of photographic computed using model atmospheres in the  approxima- long focus observations: the absolute photographic parallax 00 00 tion is underestimated by about 0.12 dex at the metallicity of amounts to $ = 0. 0798 0. 0033 (Heintz 1993). The abs 85 Peg. This is particularly important for the stellar position second determination is the recently improved adjustment of on the  diagram (Lebreton et al. 1999). We take into ac- parallax and orbital elements by Söderhjelm (1999) based count this correction and adopt the value [ Fe ] = −0.57 0.11 on the Hipparcos 3.25 yr data and old ground-based observa- H A 00 00 (Thévenin 2001). The α-elements (Mg, Ca, Si, Na, Al, Ti) tions yielding $ = 0. 0825 0. 0008. With the orbit of abs have been found to be enriched with respect to the Sun in Hall (1948) and the parallax of Heintz (1993) we derive the 85 Peg A (Fuhrmann 1998; van’t Veer 2000; Fulbright 2000). In sum of masses S = 1.63 0.33 M .Usingthedatafrom 85 Peg our calculations we take account of an α-elements enrichment, Söderhjelm (1999) we obtain S = 1.49 0.09 M .Forthe 85 Peg [α/Fe] =+0.40 dex, through appropriate opacities and input sum of masses we adopt the weighted average value: mixture. We computed the effective temperature of 85 Peg B Fe using the calibrations Teff = Teff {color, [ ]} from Lejeune S85 Peg = 1.50 0.09 M . H et al. (1998) and Bessell et al. (1998). We use both the color index (R − I)and(V − I) from ten Brummelaar et al. (2000). An estimate of the mass fraction B ≡ mB/(mA +mB) is provided by long-focus astrometry (Heintz 1993): These indices are not very sensitive to the metallicity (Alonso et al. 1996). We obtain Teff B = 4100 K using (R − I)and = − = Bp = 0.44 0.01 (p.e.). Teff B 4300 K using (V I). We choose Teff B 4200 K as a representative value of the effective temperature for the Another estimate of B is provided by the spectroscopic or- secondary. bit (e.g. Underhill 1963). Combined spectroscopic obser- The luminosities are computed using the photometry of vations covering about four decades and astrometric mea- ten Brummelaar et al. (2000), the corrected Hipparcos paral- surements give the velocity semi-amplitude of the primary lax from Söderhjelm (1999) and the bolometric correction ei- −1 KA = 4.10 0.15 km s (Duquennoy & Mayor 1991). With ther from Bessell et al. (1998) or from Flower (1996). Using J. Fernandes et al.: Improved calibration of 85 Peg 531

Table 2. Photometric and spectroscopic data for 85 Peg. Table 4. Calibration parameters and global parameters of 85 Peg A and B models lying within the uncertainty boxes. The four first rows 85 Peg A 85 Peg B show the modeling parameters t85Peg is the age of the binary in Myr, Yi, Fe 1 V 5.81 0.03 8.89 0.29 [ H ]i are the initial values of respectively the helium mass fraction and Λ R 1 5.25 0.03 7.95 0.27 the metallicity, is the mixing-length parameter. The next six rows shows the theoretical values obtained for the observational constraints I 1 4.85 0.03 7.20 0.26 of Table 3 recalled in parenthesis, S is the sum of masses in solar unit, B is the mass fraction, T ff in K and L in solar unit are respectively the 2 e Teff 5524 50 K Fe effective temperature and the luminosity, [ ]s is the surface metallic- 3 H Teff 5550 50 K ity. In next rows m is the mass in solar unit, R the radius in solar unit 4 ff Te 5275 100K and Ys the helium mass fraction at the surface.

Fe 2 − . . [ H ]A 0 86 0 06 85 Peg A 85 Peg B Fe 3 − . . [ H ]A 0 69 0 05 t85Peg 9 345 500 Fe 4 − . . Yi 0.253 0.01 [ H ]A 0 9 0 1 Fe 1 − . . ten Brummelaar et al. (2000). [ H ]i 0 185 0 054 Λ . . . . 2 Axer et al. (1994). 1 80 0 05 2 14 0 10 S 1.43 (1.50 0.09) 3 van’t Veer (2000). B 0.385 (0.44 0.02) 4 Fulbright (2000). Teﬀ 5 581 (5 550 80) 4 220 (4 200 200) L 0.622 (0.616 0.02) 0.071 (0.071 0.02) Table 3. Adopted calibration constraints. Fe − . − . . − . [ H ]s 0 55 ( 0 57 0 11) 0 49

S 85 Peg 1.50 0.09 M m 0.88 0.01 0.55 0.02 B85 Peg 0.44 0.02 R 0.846 0.500 Teff A 5550 50 K Ys 0.216 0.237 Teff B 4200 200 K LA/L 0.616 0.02 / . . LB L 0 071 0 02 within their error bars. Table 4 and Fig. 1 show the calibration [ Fe ] −0.57 0.11 H A parameters and the evolutionary tracks in the HR diagram. The most amazing result concerns the masses in the system. Table 4 Bessell et al.’s (1998) results we obtain LA/L = 0.611 0.040 shows that the models predict the sum of masses with satisfac- and LB/L = 0.069 0.030 and with Flower’s (1996) results tory agreement (error of 4.6% between models and observa- we get LA/L = 0.622 0.040 and LB/L = 0.072 0.030. tions). This is also true for the mass of 85 Peg A (error of 4.5%). The agreement is satisfactory and we take the average values. The fact that the observational mass of the main component is Table 3 lists the sum of masses, mass fraction, effective in agreement with the “astrophysical” one was already pointed temperatures, luminosities and metallicities we selected to con- out by Lebreton et al. (1999). On the other hand, the mass ratio strain the models. is poorly reproduced. This has a direct influence on the predic- tion of the mass of 85 Peg B: 0.55 M from the models against ∼0.66 M from the observations. Our fit strongly suggests that 3. Modeling 85 Peg B is itself a binary B-b, with a mb ≈ 0.11 M third com- Stellar models have been computed using the  code ponent. The theoretical mass we derive for the fainter compo- (Morel 1997). The physics of the models and the calibration nent significantly differs from the astrometric result by more method employed here are described in Morel et al. (2000); than 1σ. Such disagreement between the mass determinations element diffusion and pre-main sequence evolution are taken from astrometric and from stellar modeling reveals either er- into account. We search a solution with the χ2-minimization roneous data (observational or theoretical) or a too large as- described by Lastennet et al. (1999) and Morel et al. (2000). trometrical mass determination due to an unseen component. The confidence limits of each modeling parameter, the other On the other hand, one reasonably expects a mass difference being fixed, correspond to the maximum/minimum values it between the two main sequence stars 85Peg A & B fulfilling can reach, in order that the generated models fit the observable the mass luminosity relationship (). Using the  in the V targets within their error bars. Table 4 lists the set of model- filter of Henry & Mc Carthy (1993, formula 3a) one derives a ing parameters we derive for 85 Peg A & B. Figure 1 shows the mass difference of ≈0.35 0.08 M between the components, corresponding evolutionary tracks in the  diagram. while the astrometric data predict ≈0.18 0.10 M .Thisdiffer- ence is consistent with the possibility of an unseen companion around the secondary. We emphasize that a star of 0.11 M is 4. Discussion and conclusion 35 times fainter than a 0.55 M star (Baraffe et al. 1998) and According to the χ2 minimization we achieved the first cali- does not contribute to the luminosity of 85 Peg B+b, while it bration of the visual binary system 85 Peg, i.e. we found a set affects the astrometric mass determination. Figure 1 shows the Fe ?, , , Λ , Λ . . of calibration parameters (t Yi [ H ]i A B) and theoretical evolutionary tracks for the models of 0 88 M and 0 55 M cor- masses mA and mB which give models that fit the observables responding to our best solution. We also plot the evolutionary 532 J. Fernandes et al.: Improved calibration of 85 Peg

Fig. 1. Evolutionary tracks in the H-R diagram (see text). Dashed rectangles delimit the observed uncertainty domains. Top panel: full tracks from PMS, the dotted evolutionary track is for of a 0.66 M model computed with the calibration parameters of 85 Peg B (see text). The stellar evolution sequences are initialized on the pre-main sequence soon after the deuteron ignition. The “+” denote 1 Gyr time intervals along the evolutionary tracks. Bottom left and right panels: enlargements around the observed 85 Peg A, & B loci.

track of a 0.66 M model computed with the same initial Acknowledgements. We would like to express our thanks to the chemical composition and age. Our results give a mixing- anonymous referee, for helpful comments. We would like to express length parameter for 85 Peg A slightly lower than the solar one our thanks to C. van’t Veer, R. Cayrel, F. Thévenin and E. Lastennet for illuminating discussions and helpful advices. This research has made (ΛA = 1.8againstΛ = 1.9). This could support the sug- gestion that the mixing-length parameter decreases with de- use of the Simbad data base, operated at CDS, Strasbourg, France. creasing mass made by Lebreton et al. (2001) in the case of This work has been performed using the computing facilities provided by the OCA program “Simulations Interactives et Visualisation the Hyades cluster. This is however in disagreement with re- en Astronomie et Mécanique (SIVAM)”. This work was partially sup- sults from the 2D simulations where the mixing-length param- ported by the “Convénio ICCTI-Embaixada de Fran¸ca” (B0-60) and ff eter appears to decrease with increasing e ective temperature by the project “PESO/P/PRO/15128/1999” from “Funda¸cão para a (Ludwig et al. 1999). According to our calibration 85 Peg is Ciência e Tecnologia”. older than the Sun and is under-abundant in helium with respect to the Sun, which is consistent with what is expected for an old star in the Galaxy (Perrin et al. 1977). We point out that, References due to element diffusion during evolution, our results show an Alonso, A., Arribas, S., & Martinez-Roger, C. 1996, A&A, 291, 895 observed metallicity at the surface of 85 Peg A and B consider- Axer, M., Fuhrmann, & Gehren, T. 1994, A&A, 291, 896 ably lower than the initial value, giving a 0.3 dex depletion in Baraffe, I., Chabrier, G., Allard, F., & Hauschildt, P. H. 1998, A&A, 9Gyr. 337, 403 J. Fernandes et al.: Improved calibration of 85 Peg 533

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